Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Some Fixed Points Results of Quadratic Functions in Split Quaternions Tue, 23 Aug 2016 09:47:34 +0000 We attempt to find fixed points of a general quadratic polynomial in the algebra of split quaternion. In some cases, we characterize fixed points in terms of the coefficients of these polynomials and also give the cardinality of these points. As a consequence, we give some simple examples to strengthen the infinitude of these points in these cases. We also find the roots of quadratic polynomials as simple consequences. Young Chel Kwun, Mobeen Munir, Waqas Nazeer, and Shin Min Kang Copyright © 2016 Young Chel Kwun et al. All rights reserved. Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions Mon, 22 Aug 2016 14:11:41 +0000 We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: and , where , , is continuous, for , and for . Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. An example is also included to illustrate the main results obtained. Jian Chang, Jian-Ping Sun, and Ya-Hong Zhao Copyright © 2016 Jian Chang et al. All rights reserved. Adjoining a Constant Function to -Dimensional Chebyshev Space Wed, 17 Aug 2016 09:10:49 +0000 This paper is concerned with extending a Chebyshev system of continuous nonconstant functions into a set of functions including a constant function. Necessary and sufficient conditions for the new set to be a Chebyshev system are discussed and some results are obtained. Mansour Alyazidi-Asiry Copyright © 2016 Mansour Alyazidi-Asiry. All rights reserved. Approximation by First-Order Linear Differential Equations with an Initial Condition Mon, 15 Aug 2016 12:50:58 +0000 We will consider a continuously differentiable function satisfying the inequality for all and for some and some . Then we will approximate by a solution of the linear equation with . Jaiok Roh and Soon-Mo Jung Copyright © 2016 Jaiok Roh and Soon-Mo Jung. All rights reserved. Ulam’s Type Stability and Fixed Points Methods 2016 Mon, 08 Aug 2016 16:39:38 +0000 Janusz Brzdęk, Liviu Cădariu, Krzysztof Ciepliński, Ajda Fošner, Zbigniew Leśniak, and Bing Xu Copyright © 2016 Janusz Brzdęk et al. All rights reserved. Survey on Recent Ulam Stability Results Concerning Derivations Mon, 08 Aug 2016 10:00:13 +0000 This is a survey presenting the most significant results concerning approximate (generalized) derivations, motivated by the notions of Ulam and Hyers-Ulam stability. Moreover, the hyperstability and superstability issues connected with derivations are discussed. In the section before the last one we highlight some recent outcomes on stability of conditions defining (generalized) Lie derivations. Janusz Brzdęk, Liviu Cădariu, Krzysztof Ciepliński, Ajda Fošner, and Zbigniew Leśniak Copyright © 2016 Janusz Brzdęk et al. All rights reserved. On the Hyers-Ulam Stability of the First-Order Difference Equation Thu, 04 Aug 2016 12:24:30 +0000 We prove Hyers-Ulam stability of the first-order difference equation of the form , where is a given function with some moderate features. Moreover, we introduce some conditions for the function under which the difference equation is not stable in the sense of Hyers and Ulam. Soon-Mo Jung and Young Woo Nam Copyright © 2016 Soon-Mo Jung and Young Woo Nam. All rights reserved. On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces Thu, 04 Aug 2016 12:22:53 +0000 We study some multilinear operators with rough kernels. For the multilinear fractional integral operators and the multilinear fractional maximal integral operators , we obtain their boundedness on weighted Morrey spaces with two weights when or . For the multilinear singular integral operators and the multilinear maximal singular integral operators , we show they are bounded on weighted Morrey spaces with two weights if and bounded on weighted Morrey spaces with one weight if for . Sha He and Xiangxing Tao Copyright © 2016 Sha He and Xiangxing Tao. All rights reserved. Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class Wed, 03 Aug 2016 14:11:14 +0000 Let be a quasiconformal mapping whose Jacobian is denoted by and let be the space of exponentially integrable functions on . We give an explicit bound for the norm of the composition operator : and, as a related question, we study the behaviour of the norm of in the exponential class. The property of is the counterpart in higher dimensions of the area distortion formula due to Astala in the plane and it is the key tool to prove the sharpness of our results. Fernando Farroni and Raffaella Giova Copyright © 2016 Fernando Farroni and Raffaella Giova. All rights reserved. On the Stability of Alternative Additive Equations in Multi--Normed Spaces Mon, 01 Aug 2016 07:19:39 +0000 We introduce the notion of multi--normed space () and study the stability of the alternative additive functional equation of two forms in this type of space. Xiuzhong Yang, Jing Ma, and Guofen Liu Copyright © 2016 Xiuzhong Yang et al. All rights reserved. Fixed Point Theorems for Generalized Mizoguchi-Takahashi Graphic Contractions Sun, 31 Jul 2016 13:48:11 +0000 Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi -contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in -chainable metric space are also discussed. Nawab Hussain, Jamshaid Ahmad, and Marwan Amin Kutbi Copyright © 2016 Nawab Hussain et al. All rights reserved. Existence Results for Fuzzy Partial Differential Inclusions Sun, 31 Jul 2016 06:00:18 +0000 We discuss the existence of solution of a certain type of fuzzy partial differential inclusions with local conditions of integral types. Nayyar Mehmood and Akbar Azam Copyright © 2016 Nayyar Mehmood and Akbar Azam. All rights reserved. New Inner Product Quasilinear Spaces on Interval Numbers Tue, 26 Jul 2016 14:42:05 +0000 Primarily we examine the new example of quasilinear spaces, namely, “ interval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results on interval space related to these concepts. Secondly, we present , and quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis. Hacer Bozkurt and Yılmaz Yilmaz Copyright © 2016 Hacer Bozkurt and Yılmaz Yilmaz. All rights reserved. Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators Tue, 26 Jul 2016 13:45:18 +0000 We characterize the weighted local Hardy spaces related to the critical radius function and weights by localized Riesz transforms ; in addition, we give a characterization of weighted Hardy spaces via Riesz transforms associated with Schrödinger operator , where is a Schrödinger operator on () and is a nonnegative function satisfying the reverse Hölder inequality. Hua Zhu Copyright © 2016 Hua Zhu. All rights reserved. Stability of a Quartic Functional Equation in Restricted Domains Tue, 26 Jul 2016 10:03:53 +0000 Let be a real normed space and a Banach space and . We prove the Ulam-Hyers stability theorem for the quartic functional equation in restricted domains. As a consequence we consider a measure zero stability problem of the above inequality when . Jaeyoung Chung and Yu-Min Ju Copyright © 2016 Jaeyoung Chung and Yu-Min Ju. All rights reserved. Existence and Asymptotic Behaviour of Solutions of Differential and Integral Equations in Some Function Spaces 2016 Mon, 25 Jul 2016 12:37:03 +0000 Józef Banaś, Leszek Olszowy, Kishin Sadarangani, Asadollah Aghajani, and Mohamed A. Taoudi Copyright © 2016 Józef Banaś et al. All rights reserved. On the Existence of Coincidence and Common Fixed Point of Two Rational Type Contractions and an Application in Dynamical Programming Mon, 25 Jul 2016 09:05:01 +0000 We establish some coincidence point results for self-mappings satisfying rational type contractions in a generalized metric space. Presented coincidence point theorems weaken and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results apply, in particular, to the study of solvability of functional equations arising in dynamic programming. Ahmed H. Soliman and Tamer Nabil Copyright © 2016 Ahmed H. Soliman and Tamer Nabil. All rights reserved. On the Stability of Quadratic Functional Equations in -Spaces Mon, 25 Jul 2016 07:36:51 +0000 The Hyers-Ulam-Rassias stability of quadratic functional equation and orthogonal stability of the Pexiderized quadratic functional equation in -spaces are proved. Xiuzhong Yang Copyright © 2016 Xiuzhong Yang. All rights reserved. SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions Thu, 21 Jul 2016 11:31:46 +0000 The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. Finally, we give an example to illustrate. Pengju Duan Copyright © 2016 Pengju Duan. All rights reserved. Optimal Bounds for Gaussian Arithmetic-Geometric Mean with Applications to Complete Elliptic Integral Wed, 20 Jul 2016 11:27:25 +0000 We present the best possible parameters and such that the double inequalities , , hold for all with , where , , and are the arithmetic, quadratic, and Gauss arithmetic-geometric means of and , respectively. As applications, we find several new bounds for the complete elliptic integrals of the first and second kind. Hua Wang, Wei-Mao Qian, and Yu-Ming Chu Copyright © 2016 Hua Wang et al. All rights reserved. Singularities for One-Parameter Null Hypersurfaces of Anti-de Sitter Spacelike Curves in Semi-Euclidean Space Tue, 19 Jul 2016 11:09:36 +0000 We consider one-parameter null hypersurfaces associated with spacelike curves. The spacelike curves are in anti-de Sitter 3-space while one-parameter null hypersurfaces lie in 4-dimensional semi-Euclidean space with index 2. We classify the generic singularities of the hypersurfaces, which are cuspidal edges and swallowtails. And we reveal the geometric meanings of the singularities of such hypersurfaces by the singularity theory. Yongqiao Wang, Donghe Pei, and Ruimei Gao Copyright © 2016 Yongqiao Wang et al. All rights reserved. On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments Mon, 18 Jul 2016 13:36:07 +0000 This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included. Youliang Fu, Yazhou Tian, Cuimei Jiang, and Tongxing Li Copyright © 2016 Youliang Fu et al. All rights reserved. Characterization of Reflexivity by Convex Functions Sun, 17 Jul 2016 12:55:23 +0000 A new convexity property of convex functions is introduced. This property provides, in particular, a characterization of the class of reflexive Banach spaces. Zhenghua Luo and Qingjin Cheng Copyright © 2016 Zhenghua Luo and Qingjin Cheng. All rights reserved. Fixed Point Results Satisfying Rational Type Contraction in -Metric Spaces Sun, 17 Jul 2016 06:54:25 +0000 A unique fixed point theorem for three self-maps under rational type contractive condition is established. In addition, a unique fixed point result for six continuous self-mappings through rational type expression is also discussed. Branislav Z. Popović, Muhammad Shoaib, and Muhammad Sarwar Copyright © 2016 Branislav Z. Popović et al. All rights reserved. A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces Thu, 14 Jul 2016 06:32:08 +0000 The purpose of this paper is to provide and study a best proximity point theorem for generalized non-self-Kannan-type and Chatterjea-type mappings and Lipschitzian mappings in complete metric spaces. The significant mapping in a unified form which related to contractive mappings, Kannan-type mappings, and Chatterjea-type mappings is established. We also provide some examples to illustrate the situation corresponding to the main theorem. The main result of this paper can be viewed as a general and unified form of several previously existing results. Kasamsuk Ungchittrakool Copyright © 2016 Kasamsuk Ungchittrakool. All rights reserved. Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method Wed, 13 Jul 2016 13:17:53 +0000 We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space in order to formulate the analytical solutions in a rapidly convergent series form in terms of their -cut representation. The approximation solution is expressed by -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations. Ghaleb Gumah, Khaled Moaddy, Mohammed Al-Smadi, and Ishak Hashim Copyright © 2016 Ghaleb Gumah et al. All rights reserved. Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs Wed, 13 Jul 2016 10:07:22 +0000 We are concerned with the following system of third-order three-point boundary value problems: , , , , , , , and , where and . By imposing some suitable conditions on and , we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index. Jian-Ping Sun, Xue-Mei Yang, and Ya-Hong Zhao Copyright © 2016 Jian-Ping Sun et al. All rights reserved. Abstract Theorems on Exchange of Limits and Preservation of (Semi)continuity of Functions and Measures in the Filter Convergence Setting Wed, 13 Jul 2016 06:11:26 +0000 We give necessary and sufficient conditions for exchange of limits of double-indexed families, taking values in sets endowed with an abstract structure of convergence, and for preservation of continuity or semicontinuity of the limit family, with respect to filter convergence. As a consequence, we give some filter limit theorems and some characterization of continuity and semicontinuity of the limit of a pointwise convergent family of set functions. Furthermore, we pose some open problems. Antonio Boccuto and Xenofon Dimitriou Copyright © 2016 Antonio Boccuto and Xenofon Dimitriou. All rights reserved. Dual -Mixed Geominimal Surface Area and Related Inequalities Sun, 10 Jul 2016 07:32:44 +0000 The integral formula of dual -geominimal surface area is given and the concept of dual -geominimal surface area is extended to dual -mixed geominimal surface area. Properties for the dual -mixed geominimal surface areas are established. Some inequalities, such as analogues of Alexandrov-Fenchel inequalities, Blaschke-Santaló inequalities, and affine isoperimetric inequalities for dual -mixed geominimal surface areas, are also obtained. Tongyi Ma and Yibin Feng Copyright © 2016 Tongyi Ma and Yibin Feng. All rights reserved. Topological Dual Systems for Spaces of Vector Measure -Integrable Functions Wed, 29 Jun 2016 12:11:24 +0000 We show a Dvoretzky-Rogers type theorem for the adapted version of the -summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guarantee that the space has to be finite dimensional, contrary to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals, our vector valued version of convergence in the weak topology, is equivalent to the convergence with respect to the norm. Examples and applications are also given. P. Rueda and E. A. Sánchez Pérez Copyright © 2016 P. Rueda and E. A. Sánchez Pérez. All rights reserved.